False in the sense that they do not "improve" the game. A game with bad gameplay/narrative/design is gona stay a bad game no matter the attractiveness of the characters. They cant carry that hard. Take DarkSouls/Elden Ring for example, its common that the player-created characters are goblin looking blue skinned weird things. And the game remains fantastic regardless. it doesnt matter.
But if the game is already good - my personal choice would be to have good looking characters. But thats just me.